Natural frequency
Natural frequency, measured in terms of
Overview
In analysis of systems, it is convenient to use the angular frequency ω = 2πf rather than the frequency f, or the complex frequency domain parameter s = σ + ωi.
In a mass–spring system, with mass m and spring stiffness k, the natural angular frequency can be calculated as:
In an electrical network, ω is a natural angular frequency of a response function f(t) if the Laplace transform F(s) of f(t) includes the term Ke−st, where s = σ + ωi for a real σ, and K ≠ 0 is a constant.[2] Natural frequencies depend on network topology and element values but not their input.[3] It can be shown that the set of natural frequencies in a network can be obtained by calculating the poles of all impedance and admittance functions of the network.[4] A pole of the network transfer function is associated with a natural angular frequencies of the corresponding response variable; however there may exist some natural angular frequency that does not correspond to a pole of the network function. These happen at some special initial states.[5]
In
See also
References
- ^ Bhatt, p. 122.
- ^ Desoer 1969, pp. 583–584, 600.
- ^ Desoer 1969, p. 633.
- ^ Desoer 1969, p. 635.
- ^ Desoer 1969, p. 643.
- ^ Basic Physics 2009, p. 366.
Sources
- Bhatt, P. Maximum Marks Maximum Knowledge in Physics. Allied Publishers. ISBN 9788184244441.
- Basic Physics. Prentice-Hall of India Pvt. Limited. 2009. ISBN 9788120337084.
- Desoer, Charles (1969). Basic circuit theory. McGraw-Hill. ISBN 0070165750.
Further reading
- College Physics. 2012.
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